I had the same problem. I was not syncing podcasts between my iPhone and iPad as I had video podcasts I’d watch on my iPad and audio only podcasts on my iPhone. I recently turned on syncing and have spent a couple hours cleaning up the played podcasts since my iPad was showing some podcasts as having all the episodes unplayed. It only happened for some—others were in sync right away.
At any rate, I too had some podcasts that I had been following still showing up in lists such as Station Settings. The solution was to re-follow the show and then immediately unfollow. Now that syncing is on, it appears to have made it back to the mothership and they are no longer showing up.
The setting to sync library is in the Podcasts settings within iOS Settings.